The Application of Conditional Probability to Harmonize Nuclear Cardiology Test Results

Abstract

Both exercise single photon emission computed tomography (SPECT) imaging and myocardial perfusion imaging with positron emission tomography produce multiple outcome variables. These include the stress electrocardiogram (ECG), visual perfusion assessment and quantitative myocardial blood flow. Bayes’ analysis using conditional probability allows the distillation of multiple test results into a single probability of disease for individual patients. This paper examines the application of conditional probability analysis to two noninvasive modalities that generate multiple outcome results: exercise ECG combined with SPECT imaging and vasodilator RB-82 positron emission tomography perfusion imaging combined with quantitative measure of absolute myocardial blood flow. In this manner, a single probability of disease incorporating all the available data is generated for an individual patient.

The use of multiple noninvasive tests in a patient for a specific question is becoming more common (1). While it is expected that each new piece of noninvasive information will align, the reality is that each test carries strengths and weaknesses that generate a profile of accuracy and associated false positive and false negative results. When two non-gold-standard tests produce non-concordant results, it can be difficult to chart a clinical course. Clinical guidelines for cardiac imaging rely heavily on conditional probability in the form of pre-test clinical risk assessment to maximize the incremental value of the test result. That risk classification is often the main determinant of appropriateness. Bayesian analysis of conditional probability allows the distillation of multiple pieces of information into a single probability of the presence or absence of disease. Probability becomes the common language linking the information.

Conditional probability is a mathematical statement on the probability (P) that an event will occur given prior information on what has already occurred. This is often stated as the probability of A given B. “B” is the pre-test probability, also known as the prior. “A” reflects the post-test probability of interest, such as the likelihood of coronary artery disease following a test result but incorporates all the prior information into the calculation. For nuclear imaging, this has direct impact as all patients have prior information in the form of symptoms, risk factors, physical findings and the stress test variables.

The formulae are straight forward (2):

To get the prior, a starting point is needed. That starting point is an initial risk score for CAD. In the United States, the prevalence of significant coronary artery disease (CAD) is 7% (3). In Japan it is closer to 4% (4). With no other knowledge, an adult patient would have a 4–7/100 chance of having CAD depending on the country they reside in. But it is clear that there are risk factors which markedly impact that risk: hypertension, diabetes, lipid status, smoking and family history among others.

From these variables gathered routinely, a clinical risk score (CRS) for CAD can be calculated using one of a number of scoring models for patients with (5) and for those without (6) chest pain. Each has its own strengths and weaknesses. The key point is that they provide a risk probability for an individual patient.

The case of exercise SPECT myocardial perfusion imaging

The modality of exercise nuclear single photon emission computed tomography (SPECT) imaging has two components that generate separate results: The exercise electrocardiogram (ECG) and the myocardial perfusion images. It is known that SPECT imaging has the higher accuracy in detecting the presence of significant CAD compared to exercise electrocardiography (7). However, it is also known that exercise electrocardiography can provide comprehensive information in some scenarios, limiting the contribution of the SPECT images (8). Consequently, the ECG results cannot simply be dismissed. An alternative approach is to use conditional probability as a means to incorporate both.

Figure 1 is a graphic depiction of conditional probability. It is a display of the accuracy of exercise treadmill testing as a function of the risk of CAD of the individual being tested. The two opposing curves represent the post-test probability of CAD for a positive or negative test result as defined by a dichotomous variable-usually 1mm ST depression but it could be a Duke treadmill score or an exercise duration threshold. For any prior risk, a post-test probability is calculated. At either extreme of the curves, the pre-test and post-test probability do not change much but there is significant movement in the intermediate risk zone from pre-test to post-test. This is the basis for guidelines being slanted to favor testing of intermediate risk patients. The separation magnitude of the curves is a function of the accuracy of the test. This is reflected in the area circumscribed by the two curves: the greater the area, the more accurate the test. For this particular example, the pooled accuracy of 24 studies of exercise ECG testing was used to derive the accuracy of exercise ECG: sensitivity = 68% and specificity = 77% (9) with an area of 32%. The same curves are shown for the accuracy of myocardial perfusion imaging using SPECT Tc-99m sestamibi imaging (sensitivity=86%, specificity =74% area (10). The higher accuracy of SPECT imaging is evident in the wider displacement of the positive and negative curves and consequently the increase in area between the curves, 32% vs 44% (Figure 1B).

But what happens when there are two test results for a single test such as the stress ECG and the SPECT image interpretation? One approach to handling these two pieces of information is to interpret them as confirmatory when they agree, and favor the one with the greater accuracy when they conflict, perhaps with some adjustment for the clinical risk. An alternative approach is to maintain the clinical risk assessment formally and incorporate one of the tests into the pre-test probability with it when evaluating the second test, particularly when they are acquired in sequence (Figure 1). In this manner, the post-test probability of the first test becomes the pre-test probability of the second test (11).

Consequently, the post-test P of the exercise ECG result becomes the pre-test P for the SPECT analysis. Figure 1 demonstrates the shift in the prior P for SPECT imaging and the impact on the post-test P. The key intervention is that SPECT does not use the clinical risk score as the prior. It uses the CRS combined with the exercise ECG post-test P. The CRS is still present, but it is now a function of the exercise ECG result. This approach has shown to improve the performance of computed tomography (CT) coronary angiography (11).

PET imaging for the identification of three vessel disease

The same approach can be used to better predict which patients that undergo positron emission tomography cardiac stress testing have three vessel disease. Myocardial perfusion imaging is a relative technique in that the reconstruction algorithm identifies the highest count region and sets all the pixels as a percent of this maximal value. Consequently, if all three territories are abnormal, there will be false negative values in identifying hypo-perfused zones at rest or during hyperemia (12). PET perfusion imaging has the potential to provide absolute values of myocardial blood flow (MBF) with the dynamic acquisition of the arterial input function (bolus tracking of radionuclide as it traverses the heart) and modeling of the resultant time activity curves in individual coronary segments. In this manner, quantitative MBF provides incremental information to the visual perfusion assessment (13). But how best to harmonize these two pieces of information into a single probability of severe CAD?

For any analysis of conditional probability, a starting point must be identified. There are several studies which have examined clinical predictors of three vessel/left main disease (3V/LMT) available from the history, physical exam and rest electrocardiogram (14). These risk scores can be used to classify the initial risk of an individual patient before considering the positron emission tomography (PET) results.

Once clinical risk is established, the sensitivity and specificity of visual PET analysis can be applied. For the identification of 3V/LMT this is usually a logistic regression model that identifies independent variables associated the prediction (8). The accuracy of cardiac PET imaging is superior to SPECT for the detection of significant CAD (15). However, the prediction of the presence of 3V/LMT is more difficult. Using the summed stress score (SSS) from the visual interpretation of the perfusion images resulted in a sensitivity and specificity of 75% and 60% (16). Adding absolute MBF measures to the analysis increased the accuracy significantly: sensitivity=82%, specificity=78%. Consequently, we can use these accuracy values to provide a single probability of the presence of severe CAD in an individual patient using both pieces of information: visual myocardial uptake and absolute MBF.

Figure 2 shows the added synergy of using the PET model which incorporates SSS, visual perfusion score with the quantitative absolute myocardial blood flow (QMBF) data. For any clinical risk of 3V/LMT, a single probability can be generated using both the visual and quantitative PET results. This alleviates the problem of discordant results as a final P can always be obtained for an individual patient.

Concordance and discordance

Figure 3 shows the interplay of sequential test results on probabilities of 3V/LMT disease using this approach. When the two results align: both PET SSS and QMBF are positive or negative, the synergy is strong. For example, a patient with a pretest probability 50% has a post-test probability of 86% with a positive SSS and QMBF result and only about a 10% probability of severe disease with two negative results. However, when there is discord (positive SSS, negative QMBF or the reverse, probabilities remain in the intermediate zone (25–60%-see Figure 3).

It is evident that the utilization of conditional probability (through Bayes’ Theorem) allows the synthesis of multiple pieces of information, all of which are clinically relevant, into a single final probability for an individual patient. Using the example of coronary computed angiography and CT coronary flow reserve measures, this methodology was more accurate in identifying patients with significant CAD than either technique alone (11). This needs to be confirmed for PET using angiographic 3V/LMT disease as the end-point.

There are other modalities where multiple results are generated from a single exam (stress echo, stress MRI, and invasive FFR with coronary ultrasound). Consequently, the use of conditional probability to assimilate these dual results will continue to grow and clinicians should begin to familiarize themselves with the simple principles of Bayes’ Theorem.

Acknowledgments

This paper is dedicated to Keiichiro Yoshinaga MD, PhD for his help and inspiration

Sources of funding

None.

Conflicts of interest

None.

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